Here is a cross composed of five congruent squares. If the distance x = 10, find the area of the cross.
Geometry
Impossible Rectangle
Is it possible for a rectangle with a 48 cm perimeter to have an area of 150 square cm? Explain.
Overlapping Parallelograms
At left we have intersecting parallelograms ABCD and AFCE. Which of the sixteen numbered angles are necessarily the same size as angle #1?
Area Ratio, Circle and Square 2
A circle and a square have the same area. What is the ratio of the area of a square inscribed in the circle to the area of a circle inscribed in the square? (Draw nice pictures.)
Perimeter Ratio, Squares
Given a circle of radius x, a square inscribed in the circle, and another square circumscribed about the circle, what is the ratio of the perimeter of the outer square to that of the inner square?
Height of Octagonal Stop Sign
Each of the eight sides of this stop sign is 12.5 inches long. How tall is the sign, from top to bottom? (It’s a regular octagon.)
Equilateral Octagon
Here is a large plywood square. You are going to cut a triangle off of each corner to make a regular octagon. The square is a inches on a side. How many inches should you come in from each corner (x in the picture) so that when you cut off the triangles, all eight sides of the resulting octagon will be equal?
Find Side of Trapezoid
In the figure, AB and CD are parallel, the measure of angle D is twice that of angle B, AD is of length a and CD is of length b. What is the length of AB in terms of a and b?
- a/2 + 2b
- 3b/2 + 3a/4
- 2a – b
- 4b – a/2
- a + b
Triangular Garden Bed, Bandstand
A triangular garden bed is going to be installed near the bandstand in the Milan town square. The high school math club has designed it. It is going to have an obtuse angle, and the three sides of the triangle are whole numbers (measured in yards). The two short sides of the triangle are 3 yards and 4 yards. How long is the longest side?
Calculating With Supplements
In the diagrams below, the points A and B are located anywhere along the rays forming ∠C, whose measure is always 40°. The points A and B are connected by a line segment to form △ABC. The point D is the intersection of the bisectors of the exterior angles at A and B.
What is the measure of ∠ADB?